The Fibonacci sequence is a list of positive integers denoted

F(1), F(2), F(3), ... where

F(1) = 1, F(2) = 1

F(n+2) = F(n) + F(n+1), for n³3

So the first 12 Fibonacci numbers are

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144

Here is a simple problem that illustrates one way Fibonacci numbers pop up.
 You buy a female calf and she produces her first she-calf at age two years and after that produces another single she-calf every year. Moreover, each new she-calf performs the same way. How many she-calves are there after 12 years, assuming none die?

The following kinds of flowers have numbers of petals as indicated. Some are precise about their number of petals and some are averages.
• 3 petals: lily, iris.
Often lilies have 6 petals formed from two sets of 3.
• 5 petals: buttercup, wild rose, larkspur, columbine (aquilegia).
The humble buttercup has been bred into a multi-petalled form.
• 8 petals: delphiniums
• 13 petals: ragwort, corn marigold, cineraria,
• 21 petals: aster, black-eyed susan, chicory
• 34 petals: plantain, pyrethrum
• 55, 89 petals: michaelmas daisies, the asteraceae family